Solve the system of equations. 3x+4y+3z=5, 2x+2y+3z=5 and 5x+6y+7z=7

3x + 4y + 3z = 5

2x + 2y + 3z = 5

5x + 6y + 7z = 7

3 (3x + 4y + 3z) = 5.3

6 (2x + 2y + 3z) = 5.6

2 (5x + 6y + 7z) = 7.2

9x + 12y + 9z = 15 (1)

12x + 12y + 18z=30 (2)

10x + 12y + 14z = 14 (3)

3x + 9z = 15 [ (2) - (1) ]

2x + 4z = 16. [ (2) - (1) ]

2 (3x + 9z) = 15.2

3 (2x + 4z) = 16.3

6x + 18z = 30

6x + 12z = 48

6z = - 18 = > z = - 3 and 6x + 18z = 30 so x = [30 - 18. (-3) ] : 6 = 14

We have 2x + 2y + 3z = 5 = > 2.14 + 2y + 3. (-3) = 5 = => y = - 7

The answer is x = 14, y = - 7, z = - 3